# c1825 ORIGINAL HANDWRITTEN MANUSCRIPT BOOK OF MATHEMATICAL RULES, CASES, EXAMPLES, AND DIAGRAMS RELATING TO THE ELEMENTS OF GEOMETRY AND TRIGONOMETRY IN LAND SURVEYING

9080On offer is a beautiful and very well preserved 1825 book of mathematics relating to various aspects of geometry, trigonometry, surveying and more. The book is an excellent addition to the collection of those who delight in seeing the products of education in first half of 19th century. “Geometrical Problems” which include boxes devoted to “parallel lines,” “to bisect or divide a given line in the middle” or “to draw an angle of 15 degrees” and a diagram below the words showing a drawing of that stated geometry. The next section is under the title “Mensuration of Superficies.” This is divided into three parts, each with a number of rules, diagrams, problems, and solutions. For example: “Case 4th. To find the area of any triangle; Rule. Multiply the base by the perpendicular height and half the product will be the area. Example. What is the area of a triangle whose sides are 12, 14, and 16 rods.” Following this example, a diagram is drawn of the triangle and the problem is solved next to the diagram. At the end of each section, there are a number of “Miscellaneous Questions” that the student answers. The following section labelled “Surveying” is by far the longest in the book. It is 35 pages in length, and covers a very indepth and comprehensive amount of mathematical rules and cases needed to understand how to survey. Each question tends to get its own page, with the question at the time, mathematical calculations and charts under that, and finally a diagram taking up the bottom half or so of the page that the student used to do the equations. For example: “To survey a field with the chain only Required the content of a field whose dimensions are given in the following Field Book No. 2.” The student apparently used a number of these “Field Books” to get the data to answer the question properly. The questions use many different ways of measuring, including “Diagonals,” “Perpendiculars,” “Links” per side, “Bearings” per side, and “Distances.” For example, the answer to the question: “To survey a field, one or more of whose sides cannot be measured with the chain; as where one of the liens runs through an impassable swamp or across a pond or up the channel of a river” the student uses a chart with columns, “Stations” (labelled ‘A,’ ‘D,’ and ‘B’), “Courses” (such as ‘AB’, ‘DB’, ‘BC’, etc.), “Bearings” (‘N. 16° West,’ ‘S. 80° East,’ ‘N. 80° East,’ etc.) and “Distances” to solve for the area. Other questions include: “There is a triangular field, one side of which runs due north 4500 links and one due east 3450 links; what is the content of this field and what is the length of the broad side?”; “What is the area of an irregular four-sided field, the diagonal of which measures 75 chains and the perpendicular to the two opposite corners 23 and 28 chains?” Included in the middle of the surveying section are 2 and a half pages on rectangular and oblique “Trigonometry.” The surveying questions that follow this use this trigonometry to be solved. The charts, diagrams, and mathematics that follow are significantly more complex than the previous pages, using many more points and far more irregularly shaped fields. The section ends with a number of “Miscellaneous Questions” that require a very large amount of the complex math learned in this book to be solved. Inexplicable, after the last section of math ends, the last few pages of the book are taken up with a poem entitled “The Fall of Missolonghi” and written by “E.S.B. Channing, Esq.” The poem is 12 pages long, handwritten like the rest of the book, detailing The Third Siege of Missolonghi, which was fought in the Greek War of Independence, between the Ottoman Empire and the Greek rebels, in 1825 and 1826. I have not been able to track down either the poem nor the author in my research. It is possible it was published in a small newspaper or publication by a local poet and so has been forgotten by time. The poem is a very interesting end to the book, showing two sides to this student. The book belonged to a student with the initials, “T. A. J.” (written on both the verso and recto of the cover page in gothic lettering). His first name “Thomas” shows up on the first page of the book in the bottom right hand side. The book is very good shape. The vellum cover is about two inches longer and wider than the pages inside. The front cover contains a hand drawn diagram of a number of circles intermeshed and lines connecting various points among them. The pages are all in good shape and show a surprisingly little amount of wear or discoloration. The writing is clear and consistent throughout and the ink used has faded very little from the pages. The book is 68 pages in length, of which there is writing on 60 pages. Only the last few pages in the book have no writing on them.; Manuscript; Folio - over 12" - 15" tall; KEYWORDS: HISTORY OF, CYPHER, CYPHERING, CIPHER, EUCLIDIAN GEOMETRY, STUDENT STUDY BOOK, MATHEMATICS, TRIGONOMETRY, PLANAR GEOMETRY, MATHEMATICAL ELEMENTS IN SURVEYING, MENSURATION OF SUPERFICIES, MATHEMATICS FIELD BOOK, 19TH CENTURY EDUCATION, PRE AMERICAN CIVIL WAR, GEOMETRIC DIAGRAMS, PRACTICAL PROBLEMS IN SURVEYING, LAND SURVEYING, AMERICANA, HANDWRITTEN, MANUSCRIPT, DOCUMENT, LETTER, AUTOGRAPH, WRITER, HAND WRITTEN, DOCUMENTS, SIGNED, LETTERS, MANUSCRIPTS, HISTORICAL, HOLOGRAPH, WRITERS, AUTOGRAPHS, PERSONAL, MEMOIR, MEMORIAL, ANTIQUITÉ, CONTRAT, VÉLIN, DOCUMENT, MANUSCRIT, PAPIER ANTIKE, BRIEF, PERGAMENT, DOKUMENT, MANUSKRIPT, PAPIER OGGETTO D'ANTIQUARIATO, ATTO, VELINA, DOCUMENTO, MANUSCRITTO, CARTA ANTIGÜEDAD, HECHO, VITELA, DOCUMENTO, MANUSCRITO, PAPEL

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